Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #27161896 | C2 | semidirect |
| 2. #27161895 | C2 | semidirect |
| 3. #27161892 | C2 | semidirect |
| 4. #27161457 | C2 | semidirect |
| 5. #27161355 | C2 | semidirect |
| 6. #27161353 | C2 | semidirect |
| 7. #27161264 | C2 | semidirect |
| 8. #27161260 | C2 | semidirect |
| 9. #27161195 | C2 | semidirect |
| 10. #27161194 | C2 | semidirect |
| 11. #473×C197 | C2 | semidirect |
| 146. C197 | #3293 | semidirect |
| 154. #473 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161896 | 2 |
| #27161895 | 2 |
| #27161892 | 2 |
| #27161457 | 2 |
| #27161355 | 2 |
| #27161353 | 2 |
| #27161264 | 2 |
| #27161260 | 2 |
| #27161195 | 2 |
| #27161194 | 2 |
| #473×C197 | 2 |
| #3293 | 197 |